Does cache-control : private hurt SEO?

[shop.nordstrom]

Hi, I recently found I can no longer view our web pages in Google's cache. I get 404 errors.

http://webcache.googleusercontent.com/search?q=cache%3Ashop.nordstrom.com%2Fc%2Fwomens-shoes&rlz=1C1GGRV_enUS751US751&oq=cache%3Ashop.nordstrom.com%2Fc%2Fwomens-shoes&aqs=chrome..69i57j69i58.3575j0j4&sourceid=chrome&ie=UTF-8

I did a fetch and render in Search Console and found our header includes a "cache-control: private" entry.

The 404's started happening recently. Would this response be the culprit? If Google cannot cache the website, is this bad for SEO? On the surface of it, it sounds bad.